Question

Solve each system of equations.

6x + 5y = 10
7x - 3y = 24

Answer 1

`\begin{cases} 6x + 5y = 10 \\ 7x - 3y = 24 \end{cases}\\\begin{cases} 5y = -6x+10\ \ / :5 \\ 7x - 3y = 24 \end{cases}\\\begin{cases} y =-(6)/(5)x+2 \\ 7x - 3y = 24 \end{cases}\\\\substition \\`


`7x - 3y = 24 \\ 7x - 3 \cdot (-(6)/(5)x+2) = 24\\7x+(18)/(5)x-6=24\\ (35)/(5)x+(18)/(5)x =24 +6\\(53)/(5)x =30 \ \ / \cdot (5)/(53)\\\\x=(150)/(53)`


`y= -(6)/(5)x+2 \\y= -(6)/(5) \cdot (150)/(53) +2\\y=-(6\cdot 30)/(53)+2\\y=-(180)/(53)+ (106)/(53)\\ \\ y= -(74)/(53)\\\\ Answer : x=(150)/(53) \ \ and \ \y= -(74)/(53)`